As countless search-engine-optimization consultants can attest, Google maintains tight control over the parameters that rank the results of Internet searches. Google’s power can be terrific for those who come out on top and a torment for those who rank lower.

But expectations are different for a Google service that lets Web site operators pay to use the company’s search technology on their own properties. For those customers, Google now is sharing some control over the knobs and levers that govern search results.

Google launched the service in July under the name Custom Search Business Edition and expanded internationally in November. Now it’s got the more palatable name Google Site Search, said Nitin Mangtani, product manager for enterprise and small-business search at Google.